And in her press conference, Theresa May seemed frustrated that her proposals perhaps have not been properly digested or considered yet.

Over dinner, she said the problem could be solved by securing the type of "frictionless trade" envisaged in her Chequers plan, and that Britain was still committed to agreeing a fall-back scheme with the EU.

However, May warned it would not happen under her leadership, saying: "The UK will leave on March 29 next year".

The President of the European Council has described the Chequers agreement as unworkable at an EU summit.

But the European Union has reservations about the plan, and the two sides remain divided over how to ensure there is no hard border between the U.K.'s Northern Ireland and European Union member Ireland.

But London says this would undermine the U.K.by treating Northern Ireland differently from the rest of the country.

May promised to bring forward new proposals that would ensure trade could move freely across the Irish border, but would not require different customs regimes in Northern Ireland and the rest of the United Kingdom, a key red line for the British Prime Minister.

Tusk said a Brussels summit on October 18 would be a "moment of truth" to overcome remaining big problems and leaders pencilled in the weekend of November 17-18 to formalise a final agreement.

With barely six months until Britain leaves the bloc, at the risk of serious disruption if there is no deal to tie up legal loose ends, there is pressure on both sides: "You can hear very clearly the clock ticking in the room", said the second diplomat. In practice, to allow for parliamentary ratification, that means a deal must be struck in the next couple of months. "The Irish question needs something more than only good intentions", Tusk said.

Tusk said some elements of the British plan, known as Chequers for the country house where it was hammered out in July "indicated positive evolution in the UK's approach".

Mr Coveney made the comments as he unveiled a campaign to help Irish businesses prepare for Brexit, despite not knowing the details of any deal.

But she downplayed European Union criticism of her plans, saying: "I have always said these negotiations were going to be tough and at various stages of these negotiations, tactics would be used as part of those negotiations".

"However, the Commission's proposal for this protocol - that I should assent to a legal separation of the United Kingdom into two customs territories - is not credible", she said. "So, it would be better maybe to make another referendum and the people in the meantime could change their view".

Some leaders expressed deep frustration.

"Those who explain that we can easily live without Europe, that everything is going to be alright, and that it's going to bring a lot of money home are liars", Macron said. "Therefore, every day that is left, we must use for talks".

"Ritual dance is always a part of such negotiations", a senior adviser to one of May's summit peers told Reuters. Both sides want to show a tough face.

But their tokenistic effort was a misreading of Theresa May's political position - especially ahead of what is likely to be a hard annual conference with her own Conservative Party.

The talks, which have gone on for over a year, are bogged down in how to ensure that what will become Britain's only land border with the European Union, between Northern Ireland and Ireland, will not become home again to the checks and tensions of the past.